Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Finding Roots of Polynomials over Polynomial Quotient Rings

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93469] Re: [mg93457] Finding Roots of Polynomials over Polynomial Quotient Rings
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 10 Nov 2008 03:30:12 -0500 (EST)
  • References: <200811091025.FAA20508@smc.vnet.net>

On 9 Nov 2008, at 19:25, Julian wrote:

> Hi all,
>
> Just wondering how I would go about finding roots of an polynomial,
> say t^2 +2, over a quotient ring, say Z/5Z[x] / <x^2+2>, in
> Mathematica?  The modulus option in Reduce is only for integers, and
> I've had trouble finding anything relevant in the finite fields
> package... anyone know if this can be done in Mathematica?
>
> Thanks,
> Julian
>

Since a finite field has only finitely many elements and since the  
FiniteFields package lets you perform arithmetic on these elements,  
you can always find the roots of a polynomial simply by substituting  
all the field elements into the polynomial and selecting those that  
satisfy it. Or am I misunderstanding your question?

Andrzej Kozlowski




  • Prev by Date: Just a Curiosity (to me at least) on NMaximize and FindMaximum
  • Next by Date: webmathematica // http POST
  • Previous by thread: Finding Roots of Polynomials over Polynomial Quotient Rings
  • Next by thread: Re: Finding Roots of Polynomials over Polynomial Quotient Rings